Linear Impulsive Delay Differential Equations Research Articles

Asymptotic Behavior and Stability in Linear Impulsive Delay Differential Equations with Periodic Coefficients

We study first order linear impulsive delay differential equations with periodic coefficients and constant delays. This study presents some new results on the asymptotic behavior and stability. Thus, a proper real root was used for a representative characteristic equation. Applications to special cases, such as linear impulsive delay differential equations with constant coefficients, were also presented. In this study, we gave three different cases (stable, asymptotic stable and unstable) in one example. The findings suggest that an equation that is in a way that characteristic equation plays a crucial role in establishing the results in this study.

二阶线性脉冲中立型时滞微分方程的稳定性

二阶线性脉冲中立型时滞微分方程的稳定性

Analytic and numerical stability of delay differential equations with variable impulses

A stability theory of analytic and numerical solutions to linear impulsive delay differential equations(IDDEs) is established. The stability results in existing literature are extended to IDDEs with variable impulses. A convergent numerical process is proposed to calculate numerical solutions to IDDEs with variable impulses. Convergence and stability of the numerical solutions are studied in the paper. Numerical experiments are given in the end to confirm the conclusion.

Piecewise reproducing kernel method for linear impulsive delay differential equations with piecewise constant arguments

In this paper, we introduce a piecewise reproducing kernel method for impulsive delay differential equations with piecewise constant arguments. The method is an improved reproducing kernel method. Compared with the classical reproducing kernel method, the solutions obtained using the present method can give good approximations for a larger time interval. Some numerical examples are used to show the effectiveness and simplicity of the method.

Linear multistep methods for impulsive delay differential equations

This paper deals with the convergence and stability of linear multistep methods for a class of linear impulsive delay differential equations. Numerical experiments show that the Simpson’s Rule and two-step BDF method are of order p=0 when applied to impulsive delay differential equations. An improved linear multistep numerical process is proposed. Convergence and stability conditions of the numerical solutions are given in the paper. Numerical experiments are given in the end to illustrate the conclusion.

Modified Broström procedure in patients with generalized joint laxity

This paper deals with the convergence and stability of linear multistep methods for a class of linear impulsive delay differential equations. Numerical experiments show that the Simpson’s Rule and two-step BDF method are of order p=0 when applied to impulsive delay differential equations. An improved linear multistep numerical process is proposed. Convergence and stability conditions of the numerical solutions are given in the paper. Numerical experiments are given in the end to illustrate the conclusion.

Stability of impulsive delay differential equations

In this paper, we introduce impulsive delayed matrix function and give its norm estimation. With the help of impulsive delayed Cauchy matrix and the variation of constants method, we obtain representation of solutions to linear impulsive delay differential equations. Moreover, we derive some sufficient conditions to guarantee the trivial solution is locally asymptotically stable. Finally, two examples are given to illustrate our theoretical results.

Stability of Runge–Kutta methods for linear impulsive delay differential equations with piecewise constant arguments

This paper is concerned with a class of linear impulsive delay differential equations with piecewise continuous argument. The conditions for stability of the exact solution are obtained. Under these conditions, it is proven that the θ-method preserves stability of the equations. Furthermore, stability of Runge–Kutta methods for this kind of equations is studied. Some numerical examples are given to confirm the theoretical results.

Exponential stability of the exact solutions and the numerical solutions for a class of linear impulsive delay differential equations

This paper is concerned with exponential stability of a class of linear impulsive delay differential equations (IDDEs). Exponential stability of this kind of equations is studied by the properties of delay differential equations (DDEs) without impulsive perturbations. When different delay differential equations (DDEs) without impulsive perturbations are chosen, different sufficient conditions for exponential stability of the linear impulsive delay differential equations (IDDEs) are provided. Numerical methods for this kind of equations are constructed. The convergence and exponential stability of the numerical solutions are studied and some experiments are given.

Oscillation properties of higher order linear impulsive delay differential equations

Oscillation properties of higher order linear impulsive delay differential equations

Exponential Stability of Impulsive Delay Differential Equations

The main objective of this paper is to further investigate the exponential stability of a class of impulsive delay differential equations. Several new criteria for the exponential stability are analytically established based on Razumikhin techniques. Some sufficient conditions, under which a class of linear impulsive delay differential equations are exponentially stable, are also given. An Euler method is applied to this kind of equations and it is shown that the exponential stability is preserved by the numerical process.

Asymptotic Stability of a Class of Impulsive Delay Differential Equations

This paper is concerned with a class of linear impulsive delay differential equations. Asymptotic stability of analytic solutions of this kind of equations is studied by the property of delay differential equations without impulsive perturbations. New numerical methods for this kind of equations are constructed. The convergence and asymptotic stability of the methods for this kind of equations are studied.

A survey on oscillation of impulsive delay differential equations

This paper presents a systematic development of the oscillatory results for the linear and nonlinear impulsive delay differential equations. We also discuss linearized oscillation theory, and give some applications to mathematical biology.

The Euler scheme and its convergence for impulsive delay differential equations

This paper presents a fixed stepsize Euler scheme for linear impulsive delay differential equations and considers its convergence. We propose a method to take the partition nodes for the Euler scheme. Employing the induction and the technique of inequality, we obtain the order of convergence for Euler scheme. An example is given to illustrate the efficiency of our result.

Oscillations of even order linear impulsive delay differential equations

In this paper, we devote to investigation of even order impulsive delay differential equations, new oscillation criteria for every solution of equations are established.

Linearized oscillation of nonlinear impulsive delay differential equations

The main result of this paper is to show oscillations of nonlinear impulsive delay differential equations are equivalent to those of corresponding linear impulsive delay differential equations. The results of this paper generalize some well-known results in the literature.

Oscillation and Stability of Linear Impulsive Delay Differential Equations

The main results of this paper are that the oscillation and the stability of a linear impulsive delay differential equation are equivalent respectively to the oscillation and the stability of a corresponding linear delay differential equation without impulses. The results of this paper can be used to improve and derive some of the known results in the literature.